Knowing nothing but the rules of chess, I'd like to start learning a bit more. Some kind of tutorial app for my Android smartphone would be perfect as I can use it anywhere. The app should give theoretical explanations of basic concepts and thinking patterns (like controlling the center, pawn structure etc.) and preferably mix in a lot of example positions to solve. Free would be great, but I also would't have a problem with paying up to 10€ if it's worth it. Any suggestions?
Why waste your money when you've got free video repository like Youtube.
Watch this video, i think this is perhaps the best video i've ever come across to learn chess.
Some applications on playstore will definitely come handy:
There are many options on playstore but this three were one of the best options.
As for anything, just try YouTube app: I find this series of videos by Chess network particularly good.
I play at Lichess and I also recommend it, but another good free app I use for tactics exercises is ChessTempo.
It is just my preference. I find the collection of problems better. Lichess exercises are taken from blitz games analyzed by Stockfish. They are fine and free, but sometimes the selection they do with code is not accurate for a human.
The advantage Lichess has is when you do an exercise you can check the engine. This is useful to realize why the line you played fails. At ChessTempo this is not possible, but on messages you can read from other users why the solution and not any other alternative works.
I also use ChessTempo for my correspondence games, where you are allowed to check a database, to chose my moves in the opening.